The best way to turn a motor with a speed controller on and off repeatedly is to use the controller to do that. A good controller should have an electronic start/start input. If the controller doesn't have that, see if you can command zero speed. It is not the best practice to repeatedly disconnect either the power input to the controller or the power output to the motor. If you need to disconnect power, doing it at the controller input is probably preferable. The design details might indicate otherwise.
Industrial motor speed controllers (drives) typically have a potentiometer, keypad or signal input speed command that can remain undisturbed during all operation including power down. When the drive receives a start command the motor is accelerated with a preset ramp time with a current limited override. That allows the motor to accelerate to the set speed as quickly as possible without over stressing anything. Stopping is similar.
The drive is typically powered down only at the end of the day or when the operator takes a break, rarely more frequently than that. Emergency stop may be implemented with a contactor and a spring-set friction brake.